Neutrosophic Crisp Mathematical Morphology Eman.M.El-Nakeeb, 1,a Hewayda ElGhawalby, 1,b A.A.Salama, 2,c S.A.El-Hafeez 2,d 1,2 Port Said University, Faculty of Engineering, Physics and Engineering Mathematics Department, Egypt a) [email protected]b) [email protected]3,4 Port Said University , Faculty of Science, Department of Mathematics and Computer Science, Egypt c) [email protected]d) [email protected]Abstract In this paper, we aim to apply the concepts of the neutrosophic crisp sets and its operations to the classical mathematical morphological operations, introducing what we call "Neutrosophic Crisp Mathematical Morphology". Sever- al operators are to be developed, including the neutrosophic crisp dilation, the neutrosophic crisp erosion, the neutrosoph- ic crisp opening and the neutrosophic crisp closing. Moreover, we extend the definition of some morphological filters using the neutrosophic crisp sets concept. For instance, we introduce the neutrosophic crisp boundary extraction, the neutrosophic crisp Top-hat and the neutrosophic crisp Bot- tom-hat filters. The idea behind the new introduced operators and filters is to act on the image in the neutrosophic crisp domain instead of the spatial domain. Keywords: Neutrosophic Crisp Set, Neutrosophic Sets, Mathematical Morphology, Filter Mathematical Morphology. 1 Introduction In late 1960's, a relatively separate part of image analysis was developed; eventually known as "The Mathematical Morphology". Mostly, it deals with the mathematical theory of describing shapes using sets in order to extract meaningful information's from images, the concept of neutrosophy was first presented by Smarandache [14]; as the study of original, nature and scape of neutralities, as well as their interactions with different ideational spectra. The mathematical treatment for the neutrosophic phenomena, which already exists in our real world, was introduced in several studies; such as in [2]. The authors in [15], introduced the concept of the neutrosophic set to deduce. Neutrosophic mathematical morphological operations as an extension for the fuzzy mathematical morphology. In [9] Salama introduced the concept of neutrosophic crisp sets, to represent any event by a triple crisp structure. In this paper, we aim to use the idea of the neutrosophic crisp sets to develop an alternative extension of the binary morphological operations. The new proposed neutrosophic crisp morphological operations is to be used for image analysis and processing in the neutrosophic domain. To commence, we review the classical operations and some basic filters of mathematical morphology in both §2 and § 3. A revision of the concepts of neutrosophic crisp sets and its basic operations, is presented in §4 . the remaining sections, (§5, §6 and §7), are devoted for presenting our new concepts for "Neutrosophic crisp mathematical morphology" and its basic operations, as well as some basic neutrosophic crisp morphological filters. 2 Mathematical Morphological Operations: In this section, we review the definitions of the classical binary morphological operators as given by Heijmans [6]; which are consistent with the original definitions of the Minkowski addition and subtraction [4]. For the purpose of visualizing the effect of these operators, we will use the binary image show in Fig.1(b); which is deduced form the original gray scale image shown in Fig.1(a). Neutrosophic Sets and Systems, Vol. 16, 2017 57 University of New Mexico Eman.M.El-Nakeeb, Hewayda ElGhawalby, A.A. Salama, S.A.El-Hafeez. Neutrosophic Crisp Mathematical Morphology
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8 Conclusion: In this paper we established a foundation for what we
called "Neutrosophic Crisp Mathematical Morphology".
Our aim was to generalize the concepts of the classical
mathematical morphology.
For this purpose, we developed serval neutrosophic crisp
morphological operators; namley, the neutrosophic crisp
dilation, the neutrosophic crisp erosion, the neutrosophic
crisp opening and the neutrosophic crisp closing operators.
These operators were presented in two different types, each
type is determined according to the behaviour of the
seconed component of the triple strucure of the operator.
Furthermore, we developed three neutrosophic crisp
morphological filters; namely, the neutrosophic crisp
boundary extraction, the neutrosophic crisp Top-hat and
the neutrosophic crisp Bottom-hat filters.
Some promising expermintal results were presented to
visualise the effect of the new introduced operators and
filters on the image in the neutrosophic domain instead of
the spatial domain.
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